RGF, cinema video cameras basically don't use autofocus. The cinematographer has special attachments on the lenses for easy manual focus. Take a look at the cinema lenses, or the cinema versions of the Samyang/Rokinon lenses - there are gearlike focus rings that engage with other gears on a device known as a focus puller (I think - though the person doing the focus is also called a focus puller). If you notice cinema focus changes, they aren't "instantaneous", in fact they are relatively gradual to allow a smooth-looking transition from out of focus to in focus.
In filming video on a DSLR, the mirror is locked in the "up" position, and all work is done on the LCD live view. Shutters - I don't know how that works on DSLRs, I suspect most models just use the standard focal plane shutter mechanism for video. The high end cinema video cameras use electronic shutter only. I don't do video, yet, I just like knowing how things work.